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How do you calculate monthly repayments from APR?
Monthly payments are calculated as:
P = (L * t * (1+t)^n) / ((1+t)^n -1)
P is the monthly payment
L is the loan amount
t is the interest rate ((APR / 100) / 12)
n is the number of month the loan is over
So, if you borrowed £15000 over 24 months at 6.7% APR, it would work out as:
P = (15000 * ((6.7/100)/12) * (1+((6.7/100)/12))^24) / ((1+((6.7/100)/12))^24 -1)
P = (15000 * 0.00558 * (1+0.00558)^24) / ((1+0.00558)^24 -1)
P = (15000 * 0.00558 * 1.14297) / (1.14297 -1)
P = (95.72347) / (0.14297)
P = 669.55
So your monthly payment, over 24 months is £669.55 per month.
669.55 * 24 = 16,069.21
Meaning that in total you'll pay £1,069.21 in interest.
Remember that the term APR also includes any setup fees incurred when taking out a loan, the formula for that is slightly more complex, and the calculators here do not that that into account. For example, if your credit card has a yearly fee then that fee must be taken into account when the APR is published. The APR in that case depends upon the balance of the card (eg, if the outstanding balance is £100, and the yearly fee is £25, it will immediately add 25% to the APR, but if the balance is £1000, it'll only add 2.5% to the APR, although the actual fee is that same). As far as I'm aware, there is no "standard" was of calculating this, although I understand the financial industry are attempting to simplify it!
In a nutshell, the APR can be misleading. the "Total cost" of the loan (how much you have to pay back) is more informative.
If we're calculating the monthly interest of a loan (rather than the repayments), it's slightly easier:
P = (((outstanding balance / 100) * APR) / 365) * days in month
How do you calculate the Lottery results?
Firstly. I don't calculate the Lottery results. I guess them! However, there are a few set parameters which I use. These were taken from Lottery results between November 2002 and May 2003 (my lottery emulator used to be on another web site), and it's possible they're a little out of date these days as lottery sales have eased off.
However, in case you're interested, they are as follows:
Maximum number of ticket sales on a Saturday: 39,500,000
Minimum number of ticket sales on a Saturday: 38,000,000
Maximum number of ticket sales on a Wednesday: 21,000,000
Minimum number of ticket sales on a Wednesday: 20,000,000
Extra sales due to rollover: 10%
The following are guesses about the way the National Lottery allocate prizes. I have to admit that I've never really looked into it in much detail, but these figures appear to give realistic(ish) results
Total prize fund: 44.9% of sales
Prize fund for jackpot = (total prize fund - 3 ball winners) / 2 * 1.08
Prize fund for 5 + bonus = 34% of remaining prize fund
Prize fund for 5 balls = 20% of remaining prize fund
Prize fund for 4 balls = 46% of remaining prize fund